Finite element procedures for computing normals and mean curvature on\n triangulated surfaces and their use for mesh refinement

2017/03/16 by Mirza Cenanovic, Cenanovic, Mirza, Peter Hansbo +3 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1703.05745

openalex publication_date 2017/03/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/01

Abstract

In this paper we consider finite element approaches to computing the mean\ncurvature vector and normal at the vertices of piecewise linear triangulated\nsurfaces. In particular, we adopt a stabilization technique which allows for\nfirst order L²-convergence of the mean curvature vector and apply this\nstabilization technique also to the computation of continuous, recovered,\nnormals using L²-projections of the piecewise constant face normals.\nFinally, we use our projected normals to define an adaptive mesh refinement\napproach to geometry resolution where we also employ spline techniques to\nreconstruct the surface before refinement. We compare or results to previously\nproposed approaches.\n

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